Two angles measure `(25^(@)- a) and (135^(@) + 2a)`. If each one is the supplement of the other, then the value of a is

Options

A. `45^(@)`
B. `35^(@)`
C. `20^(@)`
D. `65^(@)`

Answer

To solve the problem, we need to find the value of \( a \) given that the two angles \( (25^\circ - a) \) and \( (135^\circ + 2a) \) are supplementary. This means their sum is equal to \( 180^\circ \).

### Step-by-step Solution:

1. **Write down the equation for supplementary angles**:
Since the angles are supplementary, we can set up the equation:
\[ (25^\circ - a) + (135^\circ + 2a) = 180^\circ \]

2. **Combine like terms**:
Now, let's simplify the left side of the equation:
\[ 25^\circ + 135^\circ - a + 2a = 180^\circ \]
This simplifies to:
\[ 160^\circ + a = 180^\circ \]

3. **Isolate \( a \)**:
Next, we need to isolate \( a \) by subtracting \( 160^\circ \) from both sides:
\[ a = 180^\circ - 160^\circ \]

4. **Calculate the value of \( a \)**:
Performing the subtraction gives us:
\[ a = 20^\circ \]

5. **Final answer**:
Thus, the value of \( a \) is:
\[ \boxed{20^\circ} \]